Problem: If $x \bigtriangleup y = 4x-2y$ and $x \veebar y = 2x-6y$, find $(-5 \bigtriangleup -4) \veebar 2$.
Solution: First, find $-5 \bigtriangleup -4$ $ -5 \bigtriangleup -4 = (4)(-5)-(2)(-4)$ $ \hphantom{-5 \bigtriangleup -4} = -12$ Now, find $-12 \veebar 2$ $ -12 \veebar 2 = (2)(-12)-(6)(2)$ $ \hphantom{-12 \veebar 2} = -36$.